Our construction closely parallels, mutatis mutandis, the QFT of fermion mixing in curved space developed in the ref. [1]}. Adjoining field mixing and curved space quantization results in a complex scenario, where the existence of infinitely many unitarily inequivalent representations of the canonical commutation relations is not only due to the mixing transformations, but also due to the intrinsic ambiguity underlying the field quantization on curved space [2]}, [3]}, [4]}, [5]}. The interplay between mixing and curvature does indeed constitute the core of our analysis.
We first construct the QFT of boson mixing in a fixed but arbitrary representation of the free fields, by appropriately generalizing the flat space procedure. We define the oscillation probabilities from the Noether charges of the Lagrangian. Then we study the transformations induced by a change in the representation of the free fields. We exhibit the invariance of local observables on the one hand and the partial invariance of oscillation probabilites on the other hand. We argue that only under specific compatibility conditions the probabilities are left invariant by a change in the representation of the free fields. Then we apply the formalism to two cosmological metrics, deriving explicitly new oscillation formulae.
